Details

Time bar (total: 21.7s)

sample282.0ms

Algorithm
intervals
Results
172.0ms103×body1280valid
66.0ms68×body640valid
12.0ms20×body320valid
9.0ms57×body80valid
3.0ms8×body160valid

simplify20.0ms

Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
02233
13533
25433
35733
done5733

prune6.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.2b

localize39.0ms

Local error

Found 4 expressions with local error:

0.2b
(sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))
0.3b
(* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))))
0.4b
(asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))
0.6b
(- (cos delta) (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))))

rewrite10.0ms

Algorithm
rewrite-expression-head
Rules
8×add-sqr-sqrt
6×pow1 add-exp-log add-cube-cbrt *-un-lft-identity add-cbrt-cube add-log-exp
3×associate-*r* associate-*l*
2×asin-acos
1×sub-neg flip3-- sin-asin diff-log pow-prod-down prod-exp sin-diff *-commutative flip-- cbrt-unprod sin-mult unswap-sqr
Counts
4 → 48
Calls
4 calls:
1.0ms
(sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))
4.0ms
(* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))))
1.0ms
(asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))
3.0ms
(- (cos delta) (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))))

series462.0ms

Counts
4 → 12
Calls
4 calls:
125.0ms
(sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))
150.0ms
(* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))))
7.0ms
(asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))
180.0ms
(- (cos delta) (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))))

simplify3.3s

Counts
60 → 60
Iterations

Useful iterations: 3 (253.0ms)

IterNodesCost
01121516
12291446
25521280
315821278
448931278
done50001278

prune392.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.1b

localize53.0ms

Local error

Found 4 expressions with local error:

0.4b
(asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))
0.4b
(asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))
0.4b
(- (* (cos delta) (cos delta)) (* (pow (sin phi1) 2) (* (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))))))
0.4b
(* (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))))

rewrite16.0ms

Algorithm
rewrite-expression-head
Rules
11×pow1
10×add-sqr-sqrt
8×add-cube-cbrt *-un-lft-identity
6×add-exp-log add-cbrt-cube add-log-exp
3×swap-sqr associate-*r* associate-*l* sin-mult
2×asin-acos associate-*r/ cos-mult
1×pow2 sub-neg sqr-cos flip3-- pow-plus diff-log pow-prod-down prod-exp associate--l+ pow-sqr *-commutative pow-prod-up frac-sub flip-- cbrt-unprod sqr-sin sub-div unswap-sqr
Counts
4 → 58
Calls
4 calls:
1.0ms
(asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))
1.0ms
(asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))
8.0ms
(- (* (cos delta) (cos delta)) (* (pow (sin phi1) 2) (* (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))))))
5.0ms
(* (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))))

series657.0ms

Counts
4 → 12
Calls
4 calls:
12.0ms
(asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))
7.0ms
(asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))
492.0ms
(- (* (cos delta) (cos delta)) (* (pow (sin phi1) 2) (* (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))))))
146.0ms
(* (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))))

simplify662.0ms

Counts
70 → 70
Iterations

Useful iterations: 2 (304.0ms)

IterNodesCost
01462808
13582451
212182063
done50002063

prune537.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.0b

localize62.0ms

Local error

Found 4 expressions with local error:

0.4b
(pow (sin phi1) 3)
0.4b
(asin (+ (* (sin delta) (* (cos phi1) (cos theta))) (* (sin phi1) (cos delta))))
0.4b
(- (pow (cos delta) 2) (+ (* (pow (sin delta) 2) (* (pow (cos phi1) 2) (* (pow (cos theta) 2) (pow (sin phi1) 2)))) (+ (* 2 (* (sin delta) (* (cos phi1) (* (pow (sin phi1) 3) (* (cos delta) (cos theta)))))) (* (pow (sin phi1) 4) (pow (cos delta) 2)))))
0.5b
(pow (sin phi1) 4)

rewrite1.5s

Algorithm
rewrite-expression-head
Rules
15×add-sqr-sqrt
13×add-log-exp
11×*-un-lft-identity
9×add-cube-cbrt
7×unpow-prod-down
6×pow1 add-exp-log pow-unpow
5×add-cbrt-cube
4×difference-of-squares
3×diff-log cube-prod sum-log sqr-pow
2×pow-to-exp pow-pow pow-exp
1×cube-mult sub-neg asin-acos flip3-- unpow3 flip-- associate--r+ distribute-lft-out-- unpow2 rem-cube-cbrt
Counts
4 → 68
Calls
4 calls:
2.0ms
(pow (sin phi1) 3)
1.0ms
(asin (+ (* (sin delta) (* (cos phi1) (cos theta))) (* (sin phi1) (cos delta))))
1.5s
(- (pow (cos delta) 2) (+ (* (pow (sin delta) 2) (* (pow (cos phi1) 2) (* (pow (cos theta) 2) (pow (sin phi1) 2)))) (+ (* 2 (* (sin delta) (* (cos phi1) (* (pow (sin phi1) 3) (* (cos delta) (cos theta)))))) (* (pow (sin phi1) 4) (pow (cos delta) 2)))))
2.0ms
(pow (sin phi1) 4)

series481.0ms

Counts
4 → 12
Calls
4 calls:
34.0ms
(pow (sin phi1) 3)
7.0ms
(asin (+ (* (sin delta) (* (cos phi1) (cos theta))) (* (sin phi1) (cos delta))))
407.0ms
(- (pow (cos delta) 2) (+ (* (pow (sin delta) 2) (* (pow (cos phi1) 2) (* (pow (cos theta) 2) (pow (sin phi1) 2)))) (+ (* 2 (* (sin delta) (* (cos phi1) (* (pow (sin phi1) 3) (* (cos delta) (cos theta)))))) (* (pow (sin phi1) 4) (pow (cos delta) 2)))))
33.0ms
(pow (sin phi1) 4)

simplify585.0ms

Counts
80 → 80
Iterations

Useful iterations: 2 (184.0ms)

IterNodesCost
01722364
14182234
214012074
done50012074

prune704.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.0b

localize68.0ms

Local error

Found 4 expressions with local error:

0.4b
(- (pow (cos delta) 2) (+ (* (pow (sin delta) 2) (* (pow (cos phi1) 2) (* (pow (cos theta) 2) (pow (sin phi1) 2)))) (+ (* 2 (* (sin delta) (* (cos phi1) (* (pow (sin phi1) 3) (* (cos delta) (cos theta)))))) (* (pow (sin phi1) 4) (pow (cos delta) 2)))))
0.5b
(pow (sin phi1) 4)
0.7b
(pow (asin (+ (* (sin delta) (* (cos phi1) (cos theta))) (* (sin phi1) (cos delta)))) 3)
7.2b
(cbrt (pow (asin (+ (* (sin delta) (* (cos phi1) (cos theta))) (* (sin phi1) (cos delta)))) 3))

rewrite1.5s

Algorithm
rewrite-expression-head
Rules
18×add-sqr-sqrt
14×*-un-lft-identity
13×add-log-exp
12×cbrt-prod add-cube-cbrt
10×unpow-prod-down
6×pow1 add-exp-log pow-unpow cube-prod
5×add-cbrt-cube
4×difference-of-squares sqr-pow
3×diff-log sum-log
2×cube-mult pow-to-exp pow-pow unpow3 pow-exp
1×sub-neg flip3-- pow1/3 flip-- rem-cbrt-cube associate--r+ distribute-lft-out-- unpow2 rem-cube-cbrt
Counts
4 → 81
Calls
4 calls:
1.5s
(- (pow (cos delta) 2) (+ (* (pow (sin delta) 2) (* (pow (cos phi1) 2) (* (pow (cos theta) 2) (pow (sin phi1) 2)))) (+ (* 2 (* (sin delta) (* (cos phi1) (* (pow (sin phi1) 3) (* (cos delta) (cos theta)))))) (* (pow (sin phi1) 4) (pow (cos delta) 2)))))
1.0ms
(pow (sin phi1) 4)
2.0ms
(pow (asin (+ (* (sin delta) (* (cos phi1) (cos theta))) (* (sin phi1) (cos delta)))) 3)
1.0ms
(cbrt (pow (asin (+ (* (sin delta) (* (cos phi1) (cos theta))) (* (sin phi1) (cos delta)))) 3))

series488.0ms

Counts
4 → 12
Calls
4 calls:
415.0ms
(- (pow (cos delta) 2) (+ (* (pow (sin delta) 2) (* (pow (cos phi1) 2) (* (pow (cos theta) 2) (pow (sin phi1) 2)))) (+ (* 2 (* (sin delta) (* (cos phi1) (* (pow (sin phi1) 3) (* (cos delta) (cos theta)))))) (* (pow (sin phi1) 4) (pow (cos delta) 2)))))
34.0ms
(pow (sin phi1) 4)
33.0ms
(pow (asin (+ (* (sin delta) (* (cos phi1) (cos theta))) (* (sin phi1) (cos delta)))) 3)
7.0ms
(cbrt (pow (asin (+ (* (sin delta) (* (cos phi1) (cos theta))) (* (sin phi1) (cos delta)))) 3))

simplify525.0ms

Counts
93 → 93
Iterations

Useful iterations: 2 (163.0ms)

IterNodesCost
01723314
14033060
213012767
done50002767

prune710.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 0.0b

regimes438.0ms

Accuracy

0% (0.1b remaining)

Error of 0.2b against oracle of 0.1b and baseline of 0.2b

bsearch0.0ms

simplify4.0ms

Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
04790
16790
done6790

end0.0ms

sample8.1s

Algorithm
intervals
Results
5.1s3113×body1280valid
1.8s1894×body640valid
452.0ms723×body320valid
319.0ms1978×body80valid
116.0ms292×body160valid